1. We showed that the anharmonicity of nuclear surface vibrations strongly influences the fusion barrier distribution by studying the effects of double phonon quadrupole and octupole excitations of ^<144>Sm on the ^<16>O+^<144>Sm fusion reactions at energies below the Coulomb barrier. Using this result, we deduced a negative quadrupole moment for both first excited 2^+ and 3^- states of ^<144>Sm. We performed a similar analysis for the ^<16>O+^<148>Sm fusion reactions. 2. We studied the influence of finite width of excited states on heavy-ion fusion reactions at energies near and below the Coulomb barrier, and showed that the finite width always reduces the enhancement effect of the channel coupling irrespective of the relative importance of the spreading and escape widths. 3. We analyzed the ^<16>O+^<154>Sm, ^<186>W ^<238>U fusion reactions at low energies and showed that.beta_6- deformation, octupole as well as beta and gamma vibrations and 2 nucleon transfer reactions play important roles. 4. We studied the bremsstrahlung in alpha decay and showed that (1) all the contributions from the classical region, tunneling region, mixed region and the wall play important roles (2) the final spectrum is given by their interference and becomes much smaller than the classical value (3) the bremsstrahlung might eliminate the ambiguity in determining the potential between the alpha particle and the daughter nucleus. 5. We showed the existence of a glory-like phenomenon caused by the shadow of a nuclear rainbow in the extremely forward angular region as a novel caustic phenomenon. 6. In addition, we studied (1) isospin dependence of nuclear incompressibility (2) screening effect by bound electrons in extremely low energy nuclear reactions (3) non-adiabatic transition in crossing two-level problems in connection with fission and heavy-ion collisions (4) electron states in metal clusters and (5) fragmentation in medium energy heavy-ion collisions.